Transversality and separation of zeros in second order differential equations
Transversality and separation of zeros in second order differential equations
Sufficient conditions on the non-linearity $f$ are given which ensure that non-trivial solutions of second order differential equations of the form $Lu=f(t,u)$ have a finite number of transverse zeros in a given finite time interval. We also obtain a priori lower bounds on the separation of zeros of solutions. In …